phpOMS/tests/Math/Matrix/EigenvalueDecompositionTest.php
2020-10-06 11:35:34 +02:00

370 lines
10 KiB
PHP

<?php
/**
* Orange Management
*
* PHP Version 7.4
*
* @package tests
* @copyright Dennis Eichhorn
* @license OMS License 1.0
* @version 1.0.0
* @link https://orange-management.org
*/
declare(strict_types=1);
namespace phpOMS\tests\Math\Matrix;
use phpOMS\Math\Matrix\EigenvalueDecomposition;
use phpOMS\Math\Matrix\Matrix;
/**
* @testdox phpOMS\tests\Math\Matrix\EigenvalueDecompositionTest: Eigenvalue decomposition
*
* @internal
*/
class EigenvalueDecompositionTest extends \PHPUnit\Framework\TestCase
{
/**
* @testdox A matrix can be checked for symmetry
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testSymmetricSymmetryMatrix() : void
{
$A = new Matrix();
$A->setMatrix([
[3, 1, 1],
[1, 2, 2],
[1, 2, 2],
]);
$eig = new EigenvalueDecomposition($A);
self::assertTrue($eig->isSymmetric());
$B = new Matrix();
$B->setMatrix([
[3, 1, 2],
[1, 2, 2],
[1, 2, 2],
]);
$eigB = new EigenvalueDecomposition($B);
self::assertFalse($eigB->isSymmetric());
}
/**
* @testdox The eigenvalues can be calculated for a symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testSymmetricMatrixEigenvalues() : void
{
$A = new Matrix();
$A->setMatrix([
[3, 1, 1],
[1, 2, 2],
[1, 2, 2],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([0, 2, 5], $eig->getRealEigenvalues()->toArray(), 0.1);
self::assertEqualsWithDelta([0, 0, 0], $eig->getImagEigenvalues()->toArray(), 0.1);
}
/**
* @testdox The V matrix of the decomposition can be calculated for a symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testSymmetricMatrixV() : void
{
$A = new Matrix();
$A->setMatrix([
[3, 1, 1],
[1, 2, 2],
[1, 2, 2],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[0, 2 / \sqrt(6), 1 / \sqrt(3)],
[1 / \sqrt(2), -1 / \sqrt(6), 1 / \sqrt(3)],
[-1 / \sqrt(2), -1 / \sqrt(6), 1 / \sqrt(3)],
], $eig->getV()->toArray(), 0.2);
}
/**
* @testdox The D matrix of the decomposition can be calculated for a symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testSymmetricMatrixD() : void
{
$A = new Matrix();
$A->setMatrix([
[3, 1, 1],
[1, 2, 2],
[1, 2, 2],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[0, 0, 0],
[0, 2, 0],
[0, 0, 5],
], $eig->getD()->toArray(), 0.2);
}
/**
* @testdox The eigenvalues can be calculated for a none-symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testNonSymmetricMatrixEigenvalues() : void
{
$A = new Matrix();
$A->setMatrix([
[-2, -4, 2],
[-2, 1, 2],
[4, 2, 5],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([-5, 3, 6], $eig->getRealEigenvalues()->toArray(), 0.1);
self::assertEqualsWithDelta([0, 0, 0], $eig->getImagEigenvalues()->toArray(), 0.1);
}
/**
* @testdox The V matrix of the decomposition can be calculated for a none-symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testNonSymmetricMatrixV() : void
{
$A = new Matrix();
$A->setMatrix([
[-2, -4, 2],
[-2, 1, 2],
[4, 2, 5],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[-\sqrt(2 / 3), \sqrt(2 / 7), -1 / \sqrt(293)],
[-1 / \sqrt(6), -3 / \sqrt(14), -6 / \sqrt(293)],
[1 / \sqrt(6), -1 / \sqrt(14), -16 / \sqrt(293)],
], $eig->getV()->toArray(), 0.2);
}
/**
* @testdox The D matrix of the decomposition can be calculated for a none-symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testNonSymmetricMatrixD() : void
{
$A = new Matrix();
$A->setMatrix([
[-2, -4, 2],
[-2, 1, 2],
[4, 2, 5],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[-5, 0, 0],
[0, 3, 0],
[0, 0, 6],
], $eig->getD()->toArray(), 0.2);
}
/**
* @testdox The decomposition can be created and the original matrix can be computed for a symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testCompositeSymmetric() : void
{
$A = new Matrix();
$A->setMatrix([
[3, 1, 1],
[1, 2, 2],
[1, 2, 2],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta(
$A->toArray(),
$eig->getV()
->mult($eig->getD())
->mult($eig->getV()->transpose())
->toArray()
, 0.2);
}
/**
* @testdox The decomposition can be created and the original matrix can be computed for a none-symmetric matrix
* @covers phpOMS\Math\Matrix\EigenvalueDecomposition
* @group framework
*/
public function testCompositeNonSymmetric() : void
{
$A = new Matrix();
$A->setMatrix([
[-2, -4, 2],
[-2, 1, 2],
[4, 2, 5],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta(
$A->toArray(),
$eig->getV()
->mult($eig->getD())
->mult($eig->getV()->inverse())
->toArray(),
0.2
);
}
public function testComplexEigenvalueDecomposition() : void
{
$A = new Matrix();
$A->setMatrix([
[3, -2],
[4, -1],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[1, 2],
[-2, 1],
], $eig->getD()->toArray(), 0.1);
self::assertEqualsWithDelta([1, 1], $eig->getRealEigenvalues()->toArray(), 0.1);
self::assertEqualsWithDelta([2, -2], $eig->getImagEigenvalues()->toArray(), 0.1);
}
public function testComplexDivision() : void
{
$A = new Matrix();
$A->setMatrix([
[-2, -4, 2],
[3, 1, -4],
[4, 5, 5],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[-0.3569, 4.49865, 0.0],
[-4.49865, -0.3569, 0],
[0.0, 0.0, 4.7139],
], $eig->getD()->toArray(), 0.1);
self::assertEqualsWithDelta([-0.35695, -0.35695, 4.7139], $eig->getRealEigenvalues()->toArray(), 0.1);
self::assertEqualsWithDelta([4.49865, -4.49865, 0.0], $eig->getImagEigenvalues()->toArray(), 0.1);
}
public function testComplexDivision2() : void
{
$A = new Matrix();
$A->setMatrix([
[-2, 3, 2],
[-4, 1, -4],
[4, 5, 5],
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[-2.5510, 0.0, 0.0],
[0.0, 3.27552, 4.79404],
[0.0, -4.7940, 3.27552],
], $eig->getD()->toArray(), 0.1);
self::assertEqualsWithDelta([-2.5510, 3.27552, 3.27552], $eig->getRealEigenvalues()->toArray(), 0.1);
self::assertEqualsWithDelta([0.0, 4.7940, -4.7940], $eig->getImagEigenvalues()->toArray(), 0.1);
}
public function testComplexDivision3() : void
{
$A = new Matrix();
$A->setMatrix([
[9, 4, 5, 1],
[-1, 15, -2, 13],
[-14, 7, 15, -13],
[13, -16, -2, 19]
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[17.7766, 14.8641, 0.0, 0.0],
[-14.8641, 17.7766, 0.0, 0.0],
[0.0, 0.0, 11.22336, 5.6595],
[0.0, 0.0, -5.6595, 11.22336]
], $eig->getD()->toArray(), 0.1);
self::assertEqualsWithDelta([17.7766, 17.7766, 11.2233, 11.2233], $eig->getRealEigenvalues()->toArray(), 0.1);
self::assertEqualsWithDelta([14.8641, -14.8641, 5.6595, -5.6595], $eig->getImagEigenvalues()->toArray(), 0.1);
}
public function testComplexDivision4() : void
{
$A = new Matrix();
$A->setMatrix([
[5, 14, 5, -6],
[13, 12, -4, -3],
[13, 10, 8, 17],
[5, -6, 3, 16]
]);
$eig = new EigenvalueDecomposition($A);
self::assertEqualsWithDelta([
[22.6519, 3.96406, 0.0, 0.0],
[-3.96406, 22.6519, 0.0, 0.0],
[0.0, 0.0, -2.1519, 3.39498],
[0.0, 0.0, -3.39498, -2.1519]
], $eig->getD()->toArray(), 0.1);
self::assertEqualsWithDelta([22.6519, 22.6519, -2.1519, -2.1519], $eig->getRealEigenvalues()->toArray(), 0.1);
self::assertEqualsWithDelta([3.96406, -3.96406, 3.39498, -3.39498], $eig->getImagEigenvalues()->toArray(), 0.1);
}
}
/*
Test case finder
$c = 0;
try {
do {
$array = [];
for ($i = 0; $i < 4; ++$i) {
$array[] = [];
for ($j = 0; $j < 4; ++$j) {
$div = \mt_rand(-20, 20);
$array[$i][] = \mt_rand(-20, 20);
}
}
$A = new Matrix();
$A->setMatrix($array);
$eig = new EigenvalueDecomposition($A);
++$c;
} while (true);
} catch (\Throwable $t) {
var_dump($c);
var_dump($array);
}
*/